EQUILIBRIUM OF RIGID BODIES 41 Second. The sum of all the torques acting upon the rigid body must vanish, that is, if Gly Q2j . . . Qn denote all the torques acting upon the body then the vector equation Gi+G2+- • • +Ga=0 (IV) must be satisfied. The following forms of the statement of these two conditions are better adapted for analysis. First. The algebraic sum of the components of all the forces along each of the axes of a rectangular system of coordinates must vanishj that is, •• +^n=0, Zn = 0. (V) Second. The algebraic sum of the components of all the torques about each of the axes of a system of rectangular coordinates must vanish} that is, (vr) 61. Coplanar Forces.— If two or more forces act in the same plane they arc said to be coplanar. If a system of coplanar forces act in the rcy-plane then the conditions of equilibrium reduce to the following equations: . . + Fn=0,J S<7,sFi(Zi + FA + - - - + Fndn = 0, . (VI) where di, 4, . . . , dn are the lever-arms of the forces FI, F2, . . . Fn? respectively, about any axis which is perpendicular to the plane of the forces. The ^-components of the forces and the x- and ^/-components of the moments; vanish identically. Consequently they need not be considered.